Merge pull request #558 from jamesray1/patch-121

Links for component types (plus update elsewhere) in block and block …

Paper.tex

@@ -334,10 +334,10 @@ \subsection{The Block} \label{ch:block}
 \item[receiptsRoot]\linkdest{receipts_Root_def_words}{} The Keccak 256-bit hash of the root node of the trie structure populated with the receipts of each transaction in the transactions list portion of the block; formally $H_{\mathrm{e}}$.
 \item[logsBloom]\linkdest{logs_Bloom_def_words}{} The Bloom filter composed from indexable information (logger address and log topics) contained in each log entry from the receipt of each transaction in the transactions list; formally $H_{\mathrm{b}}$.
 \item[difficulty] A scalar value corresponding to the difficulty level of this block. This can be calculated from the previous block's difficulty level and the timestamp; formally $H_{\mathrm{d}}$.
-\item[number]\linkdest{block_number_H_i}{} A scalar value equal to the number of ancestor blocks. The genesis block has a number of zero; formally $H_{\mathrm{i}}$.
+\item[number]\linkdest{block_number_word_def_H_i}{} A scalar value equal to the number of ancestor blocks. The genesis block has a number of zero; formally \hyperlink{block_number_H__i}{$H_{\mathrm{i}}$}.
 \item[gasLimit] A scalar value equal to the current limit of gas expenditure per block; formally $H_{\mathrm{l}}$.
 \item[gasUsed]\linkdest{block_gas_used_H__g}{} A scalar value equal to the total gas used in transactions in this block; formally $H_{\mathrm{g}}$.
-\item[timestamp]\linkdest{block_timestamp_H__s}{} A scalar value equal to the reasonable output of Unix's time() at this block's inception; formally $H_{\mathrm{s}}$.
+\item[timestamp]\linkdest{block_timestamp_word_def_H__s}{} A scalar value equal to the reasonable output of Unix's time() at this block's inception; formally \hyperlink{block_timestamp_H__s}{$H_{\mathrm{s}}$}.
 \item[extraData]\linkdest{block_extraData_H__x}{} An arbitrary byte array containing data relevant to this block. This must be 32 bytes or fewer; formally $H_{\mathrm{x}}$.
 \item[mixHash]\linkdest{mixHash_H__m}{} A 256-bit hash which, combined with the nonce, proves that a sufficient amount of computation has been carried out on this block; formally $H_{\mathrm{m}}$.
 \item[nonce]\linkdest{block_nonce_H__n}{} A 64-bit hash which, combined with the mix-hash, proves that a sufficient amount of computation has been carried out on this block; formally $H_{\mathrm{n}}$.
@@ -441,11 +441,11 @@ \subsubsection{Serialisation}
 The component types are defined thus:
 \begin{equation}
 \begin{array}[t]{lclclcl}
-H_{\mathrm{p}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{o}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{c}} \in \mathbb{B}_{20} & \wedge \\
-H_{\mathrm{r}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{t}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{e}} \in \mathbb{B}_{32} & \wedge \\
-H_{\mathrm{b}} \in \mathbb{B}_{256} & \wedge & H_{\mathrm{d}} \in \mathbb{P} & \wedge & H_{\mathrm{i}} \in \mathbb{P} & \wedge \\
-H_{\mathrm{l}} \in \mathbb{P} & \wedge & H_{\mathrm{g}} \in \mathbb{P} & \wedge & H_{\mathrm{s}} \in \mathbb{P}_{256} & \wedge \\
-H_{\mathrm{x}} \in \mathbb{B} & \wedge & H_{\mathrm{m}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{n}} \in \mathbb{B}_{8}
+\hyperlink{parent_Hash_H__p_def_words}{H_{\mathrm{p}}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{o}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{c}} \in \mathbb{B}_{20} & \wedge \\
+\hyperlink{new_state_H__r}{H_{\mathrm{r}}} \in \mathbb{B}_{32} & \wedge & H_{\mathrm{t}} \in \mathbb{B}_{32} & \wedge & \hyperlink{Receipts_Root_H__e}{H_{\mathrm{e}}} \in \mathbb{B}_{32} & \wedge \\
+\hyperlink{logs_Bloom_filter_H__b}{H_{\mathrm{b}}} \in \mathbb{B}_{256} & \wedge & H_{\mathrm{d}} \in \mathbb{P} & \wedge & \hyperlink{block_number_H__i}{H_{\mathrm{i}}} \in \mathbb{P} & \wedge \\
+\hyperlink{block_gas_limit_H__l}{H_{\mathrm{l}}} \in \mathbb{P} & \wedge & H_{\mathrm{g}} \in \mathbb{P} & \wedge & \hyperlink{block_timestamp_H__s}{H_{\mathrm{s}}} \in \mathbb{P}_{256} & \wedge \\
+\hyperlink{block_extraData_H__x}{H_{\mathrm{x}}} \in \mathbb{B} & \wedge & H_{\mathrm{m}} \in \mathbb{B}_{32} & \wedge & \hyperlink{block_nonce_H__n}{H_{\mathrm{n}}} \in \mathbb{B}_{8}
 \end{array}
 \end{equation}
 
@@ -460,10 +460,10 @@ \subsubsection{Block Header Validity}
 
 We define $P(B_{H})$ to be the parent block of $B$, formally:
 \begin{equation}
-P(H) \equiv B': \mathtt{\tiny KEC}(\mathtt{\tiny RLP}(B'_{H})) = H_{\mathrm{p}}
+P(H) \equiv B': \mathtt{\tiny KEC}(\mathtt{\tiny RLP}(B'_{H})) = \hyperlink{parent_Hash_H__p_def_words}{H_{\mathrm{p}}}
 \end{equation}
 
-The block number is the parent's block number incremented by one:
+\hypertarget{block_number_H__i}{}The block number is the parent's block number incremented by one:
 \begin{equation}
 H_{\mathrm{i}} \equiv {{P(H)_{H}}_{\mathrm{i}}} + 1
 \end{equation}
@@ -510,14 +510,14 @@ \subsubsection{Block Header Validity}
 & & H_{\mathrm{l}} \geqslant 5000
 \end{eqnarray}
 
-$H_{\mathrm{s}}$ is the timestamp (in Unix's time()) of block $H$ and must fulfil the relation:
+\hypertarget{block_timestamp_H__s}{}$H_{\mathrm{s}}$ is the timestamp (in Unix's time()) of block $H$ and must fulfil the relation:
 \begin{equation}
 H_{\mathrm{s}} > {P(H)_{H}}_{\mathrm{s}}
 \end{equation}
 
 This mechanism enforces a homeostasis in terms of the time between blocks; a smaller period between the last two blocks results in an increase in the difficulty level and thus additional computation required, lengthening the likely next period. Conversely, if the period is too large, the difficulty, and expected time to the next block, is reduced.
 
-The nonce, $H_{\mathrm{n}}$, must satisfy the relations:
+The nonce, \hyperlink{block_nonce_H__n}{$H_{\mathrm{n}}$}, must satisfy the relations:
 \begin{equation}
 n \leqslant \frac{2^{256}}{H_{\mathrm{d}}} \quad \wedge \quad m = H_{\mathrm{m}}
 \end{equation}
@@ -560,7 +560,7 @@ \section{Transaction Execution} \label{ch:transactions}
 \begin{enumerate}
 \item The transaction is well-formed RLP, with no additional trailing bytes;
 \item the transaction signature is valid;
-\item the \hyperlink{transaction_nonce}{transaction nonce} is valid (equivalent to the sender account's current nonce);
+\item the \hyperlink{transaction_nonce}{transaction nonce} is valid (equivalent to the \hyperlink{account_nonce}{sender account's current nonce});
 \item the gas limit is no smaller than the intrinsic gas, $g_0$, used by the transaction;
 \item the sender account balance contains at least the cost, $v_0$, required in up-front payment.
 \end{enumerate}
@@ -570,7 +570,7 @@ \section{Transaction Execution} \label{ch:transactions}
 \boldsymbol{\sigma}' = \Upsilon(\boldsymbol{\sigma}, T)
 \end{equation}
 
-Thus $\boldsymbol{\sigma}'$ is the post-transactional state. We also define $\Upsilon^{\mathrm{g}}$ to evaluate to the amount of gas used in the execution of a transaction, $\Upsilon^{\mathbf{l}}$ to evaluate to the transaction's accrued log items and $\Upsilon^{\mathrm{z}}$ to evaluate to the status code resulting from the transaction. These will be formally defined later.
+Thus $\boldsymbol{\sigma}'$ is the post-transactional state. We also define \hyperlink{tx_total_gas_used_Upsilon_pow_g}{$\Upsilon^{\mathrm{g}}$} to evaluate to the amount of gas used in the execution of a transaction, \hyperlink{tx_logs_Upsilon_pow_l}{$\Upsilon^{\mathbf{l}}$} to evaluate to the transaction's accrued log items and \hyperlink{tx_status_Upsilon_pow_z}{$\Upsilon^{\mathrm{z}}$} to evaluate to the status code resulting from the transaction. These will be formally defined later.
 
 \subsection{Substate}
 Throughout transaction execution, we accrue certain information that is acted upon immediately following the transaction. We call this \textit{transaction substate}, and represent it as $A$, which is a tuple: